Compare Fractions and Decimals: Is 5/6 >, <, or = to 0.9?

Fraction Comparison with Common Denominators

Choose the appropriate sign:

56?0.9 \frac{5}{6}?0.9

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose the appropriate sign
00:04 Convert from decimal to fraction
00:20 Multiply each fraction by the second denominator to find the common denominator
00:25 Make sure to multiply numerator by numerator and denominator by denominator
00:34 Now let's compare the fractions
00:40 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Choose the appropriate sign:

56?0.9 \frac{5}{6}?0.9

2

Step-by-step solution

First, let's convert 0.9 to a simple fraction.

Since there is only one digit after the decimal point, the number divides by 10 as follows:

0.9=910 0.9=\frac{9}{10}

Now we have two simple fractions with different denominators.

To compare them, note that the smallest common denominator between them is 60.

We'll multiply each one to reach the common denominator as follows:

56×1010=5060 \frac{5}{6}\times\frac{10}{10}=\frac{50}{60}

910×66=5460 \frac{9}{10}\times\frac{6}{6}=\frac{54}{60}

Now we can compare the two fractions and see that:

5060<5460 \frac{50}{60}<\frac{54}{60}

3

Final Answer

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Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert to common denominators to compare fractions accurately
  • Technique: Find LCD 60: 56=5060 \frac{5}{6} = \frac{50}{60} , 0.9=5460 0.9 = \frac{54}{60}
  • Check: Compare numerators with same denominator: 50 < 54 ✓

Common Mistakes

Avoid these frequent errors
  • Comparing fractions with different denominators directly
    Don't compare 5/6 and 9/10 by looking at numerators and denominators separately = wrong conclusion! This ignores that the parts are different sizes. Always convert to common denominators or decimals first.

Practice Quiz

Test your knowledge with interactive questions

Which decimal number is greater?

FAQ

Everything you need to know about this question

Why can't I just compare 5 and 9 to see which fraction is bigger?

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Because 5 sixths and 9 tenths are different sized pieces! You need to convert to the same size pieces (common denominator) to compare fairly.

Should I convert fractions to decimals or find a common denominator?

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Both methods work! Converting 56 \frac{5}{6} to 0.833... shows 0.833 < 0.9. Use whichever method feels more comfortable to you.

How do I find the least common denominator between 6 and 10?

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List multiples of each: 6: 6, 12, 18, 24, 30... and 10: 10, 20, 30... The first number that appears in both lists is your LCD = 30.

What if I get confused with which fraction is larger?

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Remember: with the same denominator, the fraction with the bigger numerator is larger. 5460>5060 \frac{54}{60} > \frac{50}{60} because 54 > 50!

Is there a quicker way to compare fractions?

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Yes! Cross-multiply: Compare 5 × 10 = 50 with 6 × 9 = 54. Since 50 < 54, we know 56<910 \frac{5}{6} < \frac{9}{10} .

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